Billard R, Tissot G, Gabard G, Versaevel M
Laboratoire d'Acoustique de l'Université du Mans, LAUM-Unité Mixte de Recherche (UMR) Centre National de la Recherche Scientifique (CNRS) 6613, av. Olivier Messiaen, Le Mans, 72085, France.
Institut National de Recherche en Informatique et en Automatique (INRIA) Rennes Bretagne Atlantique, Institut de Recherche Mathématique de Rennes (IRMAR)-UMR CNRS 6625, av. Général Leclerc, Rennes, 35042, France.
J Acoust Soc Am. 2021 Jan;149(1):16. doi: 10.1121/10.0002973.
In the linear regime and in the absence of mean flow, the impedance of perforated liners is driven by visco-thermal effects. In this paper, two numerical models are employed for predicting these visco-thermal losses. The first model is the linearized compressible Navier-Stokes equations (LNSE), solved in the frequency domain. The second model is the Helmholtz equation with a visco-thermal boundary condition, accounting for the influence of the acoustic boundary layers. These models are compared and validated against measurements. The quantitative analysis of the dissipation rate due to viscosity, computed from the LNSE solutions of four perforated plates, highlights significant differences between the edge effects of a macro- and a micro-perforated plate. In the latter case, a jet is present at the entrances of the perforation. In contrast, the proposed numerical method to calculate the impedance of perforated liners, based on the Helmholtz equation and a visco-thermal boundary condition, is found to be computationally cheaper and to provide reliable predictions.
在线性 regime 且无平均流的情况下，穿孔衬里的阻抗由粘热效应驱动。本文采用两种数值模型来预测这些粘热损耗。第一种模型是在频域中求解的线性化可压缩纳维 - 斯托克斯方程（LNSE）。第二种模型是具有粘热边界条件的亥姆霍兹方程，考虑了声边界层的影响。将这些模型与测量结果进行了比较和验证。从四个穿孔板的 LNSE 解计算出的由于粘性导致的耗散率的定量分析，突出了宏观和微穿孔板边缘效应之间的显著差异。在后一种情况下，穿孔入口处存在射流。相比之下，基于亥姆霍兹方程和粘热边界条件计算穿孔衬里阻抗的所提出的数值方法，被发现计算成本更低且能提供可靠的预测。
